SECTION A: ANSWER ANY FOUR QUESTIONS [EACH CARRYING 5 MARKS]
1.
A and and B are events events with with p(A – B) = 0.3, 0.3, p(A) = 0.6, 0.6, p(B p(B – A) A) = 0.2. Find Find p(A∩B). p(A∩B).
2.
Find the probabilit o! "ettin" at #ost two s$%%esses in a se&$en%e o! o! ten independent independent Berno$lli Berno$lli trials in whi%h the probabilit o! s$%%ess s$%%ess in ea%h trial trial is '0. Also !ind !ind the #ean n$#ber n$#ber o! s$%%esses and and the standard deviation deviation o! the n$#ber o! s$%%esses.
3.
Fro# a sa#ple sa#ple o! !i!t observa observations tions,, the sa#ple #ean #ean was 23.32, 23.32, and the sa#ple sa#ple standard standard deviation deviation was '.3. '.3. *onstr$%t a + %on!iden%e interval !or the pop$lation #ean.
'.
A -ois -oisson son pro% pro%ess ess has has a rate rate para#e para#eter ter λ = .. Find p( ≤ ) and p( / 3).
.
A #an$!a%t$rer %lai#s that that at #ost #ost o! the prod$%ts she prod$%es are de!e%tive. de!e%tive. n a rando# sa#ple sa#ple o! 10 $nits, 12 $nits were de!e%tive. s the #an$!a%t$rers %lai# valid
6.
Fro# the !ollow !ollowin" in" %ontin"e %ontin"en% n% table, table, %an it be %on%l$ded %on%l$ded that there there is a "ender bias in the $se o! %os#eti %os#eti%s %s
#en wo#en
$se %os#eti%s 2 0
do not $se %os#eti%s 20
SECTION B: ANSWER ANY THREE QUESTIONS [EACH CARRYING 10 MARKS]
.
' o! the st$dents o! a parti%$lar %olle"e are "irls. o! the "irls "irls o! the %olle"e passed passed in #athe#ati%s, #athe#ati%s, while while onl 6 o! the bos passed in #athe#ati%s. Find the overall per%enta"e o! st$dents who passed in #athe#ati%s. Also4 Also4 a. ! a rando#l sele%ted sele%ted st$dent is !o$nd to have passed in #athe#ati%s, #athe#ati%s, what what is the probabilit that the the st$dent is a "irl b. ! a rando#l sele%ted sele%ted st$dent is !o$nd to have have !ailed in #athe#ati%s, #athe#ati%s, what what is the probabilit probabilit that the the st$dent is a bo
.
5he hei"hts o! athletes in a pop$lation %an be ass$#ed to !ollow !ollow a nor#al distrib$tion, with a #ean o! and a standard deviation o! . . Find the per%enta"e o! athletes who wo$ld be epe%ted to be shorter than , the per%enta"e o! athletes who wo$ld be epe%ted to be between 6 and 6 in hei"ht, and the per%enta"e o! athletes who wo$ld be epe%ted to be taller than .
+.
n a rando# rando# sa#ple o! o! 20 #en, + li7ed %ho%olate i%e %rea#, whereas, whereas, in a rando# sa#ple o! 30 wo#en, wo#en, 1+0 li7ed li7ed %ho%olate i%e %rea#. s there a si"ni!i%ant di!!eren%e between the #en and wo#en in their pre!eren%e to %ho%olate i%e %rea# (at 8 = )
10. 5he #ean 9 o! a rando# sa#ple sa#ple o! 2 bos is !o$nd to be 130, with standard standard deviation 10. 5he 5he #ean 9 o! a rando# sa#ple o! 20 "irls is !o$nd to be 1'0, with standard deviation 1. *an one %on%l$de that "irls have a si"ni!i%antl hi"her 9 than bos
SECTION C: ANSWER ANY TWO QUESTIONS [EACH CARRYING 15 MARKS]
11. A #ana"er wants to deter#ine whether his distrib$tion o$tlets are per!or#in" e&$all well. :e %olle%ts sales !i"$res !ro# ea%h o! the sales#en, as !ollows4 istrib$tion >$tlets 4 Cales Fi"$res 4
A 30 30
B 2 2
* ' '
3 30
3 3
2 20 2
'0 '0 ' '0
3
;se one
?A to test whether there is a di!!eren%e between the per!or#an%es o! the distrib$tion o$tlets. 12. 5he !ollowin" data pertains to the n$#ber o! %$sto#ers arrivin" at a ban7 %ash
!re&$en% 1 6 3 10
Fit a -oisson distrib$tion to the above data, and appl the @ 2
10 2'
12 2
1' 32
16 3
1 ''
20 0
sti#ate the re"ression e&$ation o! ield on rain!all, and esti#ate the ield when the level o! rain!all is 2 ## .
